Question

Under what conditions heat can be given to a substance without raising its temperature?

Answer 1

Condensation or freezing is an exothermic process where the heat can be given.

Heat can be given to a substance without raising its temperature when a substance is changing its physical state, that is phase changes [for eg from solid to liquid and liquid to gas ].
The heat energy which has to be supplied to change the state of a substance is called its Latent Heat. Latent heat doesn't raise the temperature. But it must be supplied to change the state of the substance.

Latent means hidden heat and under conditions of vaporization and melting the heat is constantly increased but the temperature does not rises , this is because of latent heat.